Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session S5: Theory of Orbital Magnetization and Related Properties |
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Sponsoring Units: DCMP Chair: Raffaele Resta, University of Trieste Room: Morial Convention Center RO1 |
Wednesday, March 12, 2008 2:30PM - 3:06PM |
S5.00001: Theory of Orbital Magnetization and its Generalization to Interacting Systems Invited Speaker: Junren Shi Recently, a new formula for the orbital magnetization was proposed. In this talk, I will review the original derivation of the formula based on the semi-classical wave-packet dynamics, as well as a general derivation based on the standard perturbation theory of quantum mechanics. The quantum derivation clarifies the origin of the novel aspects of the semi-classical derivation, such as the Berry phase correction to the density of states. It is valid for general systems including insulators with or without a Chern number, metals at zero or finite temperatures. More importantly, we are able to combine the quantum derivation with the exact current and spin density functional theory (SCDFT), proving the validity of the formula for interacting systems. With this development, the new magnetization formula, in combination with the recent advances in the construction of optimized effective potential for SCDFT, will turn out to be a powerful practical tool for the study of systems that have long defied traditional ab-initio methods. \newline \newline [1] J. Shi, G. Vignale, D. Xiao and Q. Niu, Phys. Rev. Lett. 99, 197202 (2007). \newline [2] Z. Wang, P. Zhang and J. Shi, Phys. Rev. B 76, 094406 (2007). \newline [3] D. Xiao, J. Shi and Q. Niu, Phys. Rev. Lett., 95, 137204 (2005). [Preview Abstract] |
Wednesday, March 12, 2008 3:06PM - 3:42PM |
S5.00002: Optical sum rules for the orbital magnetization and anomalous Hall conductivity Invited Speaker: Ivo Souza Magnetic circular dichroism (MCD), the differential absorption of left- and right-circularly-polarized light by ferromagnets, results from the interplay between spin polarization and spin-orbit interaction. The same two ingredients are responsible for their spontaneous (``anomalous'') Hall conductivity (AHC) and orbital magnetization. I will discuss how the three phenomena are related by two sum rules for the interband MCD spectrum.\footnote{I. Souza and D. Vanderbilt, {\tt arXiv:0709.2389} (2007).} The sum rules are of the form $\int_0^\infty \omega^{-p}\sigma''_{{\rm A},\alpha\beta}(\omega)d\omega$, where $\sigma''_{\rm A}$ is the absorptive part of the antisymmetric optical conductivity. The sum rule with $p=0$ is the dichroic counterpart of the familiar $f$-sum rule for linearly-polarized light. I will show that it yields a contribution to the ground-state orbital magnetization which in insulators is associated with the circulation of the Wannier orbitals around their centers (more precisely, to the gauge-invariant part thereof). This differs from the net circulation, or total orbital magnetization,\footnote{ D. Xiao, J. Shi, and Q. Niu, Phys. Rev. Lett. {\bf 95}, 137204 (2005).}$^{,}$\footnote{T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta, Phys. Rev. Lett. {\bf 95}, 137205 (2005).} which has two additional contributions: (i) the remaining Wannier self-rotation, and (ii) the ``itinerant'' circulation arising from the center-of-mass motion of the Wannier orbitals. Contributions (i) and (ii) are not separately meaningful, since their individual values depend on the particular choice of Wannier functions. Their sum is however gauge-invariant, and can be inferred from a combination of gyromagnetic and magneto-optical experiments. The $p=1$ sum rule is the dc limit of the dichroic Kramers-Kronig relation which yields $\sigma'_{\rm A}(0)$, the Karplus-Luttinger AHC. {\it Ab-initio} studies have shown that it is necessary to sample over millions of $k$-points to converge the calculation of this quantity. I will describe an efficient real-space method for computating the AHC\footnote{ X. Wang, J.~R. Yates, I. Souza, and D. Vanderbilt, Phys. Rev. B {\bf 74}, 195118 (2006).} and MCD\footnote{J.~R. Yates, X. Wang, D. Vanderbilt, and I. Souza, Phys. Rev. B {\bf 75}, 195121 (2007).} using Wannier functions, and present some illustrative calculations for ferromagnets as well as field-polarized solid and liquid heavy metals.\footnote{G. Busch and H.--J. G\"untherodt, Solid State Phys. {\bf 29}, 235 (1974).} The possible role of configurational disorder in enhancing the field-induced AHC of liquid metals by introducing low-frequency Drude-related features in the MCD spectrum will be explored. [Preview Abstract] |
Wednesday, March 12, 2008 3:42PM - 4:18PM |
S5.00003: A converse approach to the calculation of NMR shielding tensors Invited Speaker: Timo Thonhauser We propose an alternative approach for computing the NMR response in periodic solids that is based on a recently developed theory of orbital magnetization [1]. Instead of obtaining the shielding tensor from the response to an external magnetic field, we derive it directly from the orbital magnetization appearing in response to a microscopic magnetic dipole [2]. Our new approach is very general, and it can be applied to either isolated or periodic systems. The converse procedure has an established parallel in the case of electric fields, where Born effective charges are often obtained from the polarization induced by a sublattice displacement instead of the force induced by an electric field. Our novel approach is simple and straightforward to implement since all complexities concerning the choice of the gauge origin are avoided and the need for a linear-response implementation is circumvented. We have demonstrated its correctness and viability by calculating chemical shieldings in simple molecular systems, finding excellent agreement with previous theoretical and experimental results. Applications to more complex systems are currently in progress. \begin{itemize} \item[(1)] T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta, Phys. Rev. Lett. 95, 137205 (2005). \item[(2)] T. Thonhauser, Arash A. Mostofi, Nicola Marzari, R. Resta, David Vanderbilt, submitted to Phys. Rev. Lett. (2007), arXiv:0709.4429v1. \end{itemize} [Preview Abstract] |
Wednesday, March 12, 2008 4:18PM - 4:54PM |
S5.00004: Non-perturbative ab-initio calculation of the g-tensor in periodic boundary conditions Invited Speaker: Davide Ceresoli Electron Paramagnetic Resonance (EPR) spectroscopy is one of the most powerful and versatile analytic tools in materials science to date. The wealth of important information available from EPR spectroscopy, however, cannot be extracted from experiments alone, rather from the combination of experimental date and theoretical calculations. To date, first principle methods for computing the EPR g-tensor rely on the linearization of the effective spin Hamiltonian with respect to spin orbit (SO) coupling [1]. While this approach gives good results for light atoms, it is insufficient when SO coupling is strong, as in transition metal compounds. We have derived a method to calculate the electronic g-tensor of paramagnetic defects from first principles in a non-perturbative way, based on the formula for the orbital magnetization [2]. The main advantage of his method, is that the external magnetic field do not enter the formula explicitly, showing that the g-tensor can be calculated as a ground state quantity by including the spin-orbit term in the SCF hamiltonian. We have found a perfect agreement with linear response calculations for bulk systems and molecular complexes containing light atoms. For heavier atoms, the agreement with experimental data is substantially improved. \newline \newline [1] C. J. Pickard and F. Mauri, Phys. Rev. Lett. 88, 086403 (2002). \newline [2] D. Ceresoli, T. Thonhauser, D. Vanderbilt and R. Resta, Phys. Rev. B 74, 024408 (2006); D. Xiao, G. Vignale, J. Shi and Q. Niu, Phys. Rev. Lett. 99, 197202 (2007). [Preview Abstract] |
Wednesday, March 12, 2008 4:54PM - 5:30PM |
S5.00005: First-principles approach to Non-Collinear Magnetism: towards Spin Dynamics Invited Speaker: E.K.U. Gross Most formulations of spin density functional theory (SDFT) restrict the magnetization vector field to have global collinearity. Nevertheless, there exists a wealth of strong non-collinearity in nature, for example molecular magnets, spin-spirals, spin-glasses and all magnets at finite temperatures. The local spin density approximation (LSDA) can be extended to these non-collinear cases [1] but this extension has the undesirable property of having the exchange-correlation (xc) field parallel to the magnetization density at each point in space. When used in conjunction with the equation of motion for the spin magnetization in the absence of spin currents and external fields [2,3], this local collinearity eliminates the torsional term, resulting in no time evolution. This severe shortcoming of LSDA, where the physical prediction is qualitatively wrong, opens up an important new direction for the development of functionals where this time evolution is correctly described. Towards this goal, I will describe our extension of the Kohn-Sham optimized effective potential (OEP) method to the non-collinear case and derive the corresponding integral equations, applicable to both finite and extended systems [3,4]. Most importantly I'll show that the resulting magnetization and xc field are not locally collinear to each other for real solids, and will therefore produce manifestly different spin-dynamics. \newline \newline [1] J.~Kuebler, K.-H.~Hoeck, J.~Sticht and A.~R.~Williams, J.~Phys.~F{\bf 18}, 469 (1993). \newline [2] K.~Capelle, G.~Vignale and B.~L.~Gyoerffy, Phys.~Rev.~Lett.{\bf 87}, 206403 (2001). \newline [3] S.~Sharma, J.~K.~Dewhurst, C.~Ambrosch-Draxl, S.~Kurth, N.~Helbig, S.~Pittalis, S.~Shallcross, L.~Nordstroem and E.K.U.~Gross Phys.~Rev.~Lett.{\bf 98}, 196405 (2007) \newline S.~Sharma, S.~Pittalis, S.~Kurth, S.~Shallcross, J.~K.~Dewhurst and E.K.U.~Gross Phys.~Rev.~B{\bf 76}, 100401 (Rapid Comm.) (2007) [Preview Abstract] |
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